As in [1]}, [2]}, [3]}, [4]}, [5]}, PFE results will be compared to the most energetic structures extracted from the flow using spectral proper orthogonal decomposition (SPOD). Following [6]}, these structures are obtained by solving the integral eigenvalue problem
\(\int \displaylimits _\Omega {S}(x,x^{\prime },r,r^{\prime },m,\omega ) \mathbf {\psi } (x^{\prime },r^{\prime },m,\omega ) r^{\prime }dr^{\prime }dx^{\prime } = \sigma (m,\omega ) \mathbf {\psi } (x,r,m,\omega ),\) 
